In most vehicles there is a need for some kind of differential in the drive train to enable a speed difference between the drive wheels when driving in tight bends. By far the most common solution to this problem is the so called open differential. However, a well-known disadvantage of open differentials occurs when one of the driven wheels engages the road surface with a low coefficient of friction [mu] while the other has a higher [mu]. In such cases, the low traction effort developed at the low [mu] contact surface prevents significant torque from being developed at the other wheel. Since the torque between the two axle shafts of an open differential is always almost equal, little total traction effort can be developed to pull the vehicle from its position.
Because of this basic disadvantage, different kinds of locking differentials have been developed. One early variant that was developed to solve this disadvantage is the manually switchable locking differential which is either fully open or fully locked. This variant, in its locked mode, gives the best possible traction in split-[mu] conditions. However, the driver himself needs to make sure the differential is in its open mode before attempting to make a tight turn for example on dry tarmac to avoid extreme loads on the drive shafts etc. as well as avoiding a strong yaw resisting moment about the yaw axis of the vehicle trying to prevent the vehicle from turning. Locking differentials of this kind are normally fitted to off road- or utility vehicles to improve low speed traction on less than perfect roads. A fully locked differential can also lead to a certain degree of self-steering behaviour in severe split [mu] situations if the input torque is high. This problem can be diminished if the driver modulates the throttle properly or if a traction control system makes the torque demand reduction for him to get the best possible compromise between traction capability and self-steering behaviour, meaning that an acceptable degree of counter steering is needed by the driver.
Similar disadvantages of the open differential can also occur in situations with a perfectly balanced [mu]-value side to side. In dynamic driving events, like turning at speed, there will be a lateral load transfer which will cause the drive wheels on either side of the vehicle to get differentiated normal forces which in more severe cornering situations can render a lightly loaded drive wheel with very little traction capacity leading to a low total traction effort despite the heavier loaded drive wheel really being able to handle much more torque than it is being subjected to by the open differential, that always divides the torque equally between both drive wheels.
In the above mentioned situation the open differential would, by changing its internal rotation direction, allow the inside drive wheel to revolve at a higher rotational speed than the corner outer drive wheel even though the latter covers a greater road distance during cornering situations. This happens due to the fact that the differentiated normal forces alter the longitudinal stiffness of each individual tire which means that the slip rate of the corner inner wheel will be substantially higher than that of the outer wheel. If you in the same situation would lock the differential it wouldn't allow the inside drive wheel to over-speed the outer but would instead, in this situation, send more than half of the torque to the corner outer drive wheel. This phenomenon is described in greater detail in the patent document WO 2006/041384, in which the mentioned rotational direction changing event is called the “cross-over-point” and the Locking Differential described is referred to as being “direction sensitive”. Hence, this kind of differential will herein be referred to as a “Direction Sensitive Locking Differential” (DSLD). In the case of the DSLD, two separate actuators are used to control the locking of the differential in each of the two potential differentiation directions. To fully lock the DSLD both actuators are excited simultaneously. There might also be a separate actuator to unlock the DSLD.
There have been many attempts to solve the above mentioned problem by designing different kinds of self-locking differentials or so called Limited Slip Differentials (LSD). These differentials can function according to different principles but probably the most common principle utilizes clutches to generate friction that can transfer torque between each output shaft by more or less locking the output shafts of the differential together. The simpler variants may have spring loaded clutch packs and the amount of spring preload, the number of active friction surfaces and the coefficient of friction will decide how much torque difference it will take for the differential to start differentiating. If this friction force is high, the traction capabilities will be good but the LSD will also induce quite a bit of extra under steer, especially when driving slowly (low lateral load transfer) in tighter corners. This means that the friction force will be a compromise that needs to be found depending on which is deemed more important.
There are more advanced clutch pack type LSD's, which typically contain actuator mechanisms including cam ramps with interchangeable angles for tuned clamping power of the clutch packs in response to the amount and direction of the input torque. These force transmitting ramps mean that the need for a static preload is far smaller and it can even be omitted completely in some cases which would mean that the LSD is practically an open differential for as long as there is no input torque. These more advanced LSD's are often used in motorsport applications and the general idea behind them is to be able to tune the amount of torque transfer during acceleration independently from the amount of torque transfer during deceleration and braking and thereby being able to tune the handling balance of the vehicle for different driving scenarios.
As previously mentioned there is lateral load transfer in response to cornering that transfers normal forces acting on the wheels and tires from the corner inner wheels to the outer wheels in the cornering situation, due to lateral acceleration. There is also longitudinal load transfer, which increases the normal force of the rear wheels at the expense of the normal force of the front wheels in response to longitudinal acceleration, or the other way around in longitudinal deceleration. This longitudinal load transfer thus invokes under steer in response to (positive longitudinal) acceleration and over steer in response to deceleration (or in other words negative longitudinal acceleration). When stating that it invokes over steer in response to deceleration it does not necessarily mean that it will become over steering, because that depends on the steady state handling balance designed in to the vehicle in the first place but rather that the balance will change in the direction towards over steer.
Racing cars, as an example, are generally tuned to have a nearly neutral steady state handling balance and they are often equipped with tuneable limited slip differentials. When they accelerate out of a corner, the corner outer drive wheel is generally much heavier loaded which means it can handle quite a bit more drive torque than the inner wheel can, which in many cases would mean that an open differential would start differentiating in the “wrong” direction which also would mean that it has passed the cross-over-point and that the differential generally for performance reasons should be locked in these situations and thereby allowing a stronger acceleration as well as giving a yaw supporting moment about the yaw axis of the vehicle and consequently counteracting the longitudinal acceleration-induced under steer. On the other hand, when a racing car is trail braking on its way into a corner the longitudinal load transfer towards the front axle will make the car potentially over steering and unstable, in this situation a locked differential would make the braking torques of the wheels of the driven axle differentiated in the way that the corner outer wheel would brake harder than the inner wheel, which would brake lighter or indeed in some cases could even have a positive drive torque if the total braking torque of the driven axle is low enough or if the yaw rate is high enough.
From this latter scenario we can see that the locked or more or less locked differential besides its traction enhancing influence also can help improve vehicle stability for example when decelerating by differentiating the longitudinal tire forces of the drive wheels and thereby giving a yaw resisting moment about the yaw axis of the vehicle.
From all this we can see that a properly tuned LSD to some extent can make the handling balance of the car more consistent by compensating for the unbalancing influences of the longitudinal accelerations when these are present and be more or less open when there is no input torque. Taking the previously mentioned effect of longitudinal accelerations and the accompanying load transfer, together with the fact that a more or less locked differential normally gives a yaw resisting effect which can turn into a yaw supporting effect if the input toque gets high enough we can draw the conclusion that the strongest yaw resisting moment can be achieved if the differentiated longitudinal forces are generated by the front axle and conversely, the strongest yaw supporting moment can be achieved if they are generated by the rear axle (presuming roughly equal tire sizes and a roughly balanced static weight distribution front to rear).
Apart from all of the above, there is of course also the other major influence on the handling balance stemming from the fact that the lateral capacity of a tire decreases as it is subjected to a (large enough) longitudinal drive force, which will invoke a drive force related, over steer tendency for rear wheel drive cars counteracting the load transfer based tendency for under steer during acceleration and conversely, which will invoke a drive force related under steer tendency for front wheel drive cars adding to the load transfer based one. If we again look at the above described situation with the racing car accelerating out of a corner. Presuming it is a rear wheel drive car, the latter of the above described influences may well take precedence over the load transfer based one making the car over steer, forcing the driver to properly modulate the throttle to avoid the car swerving out. However, it should be noted that if the driver manages this in a proper way the total amount of combined lateral and longitudinal forces that he can extract from the rear axle will be higher with the locked differential than with the open one, which actually is one of the main reasons race cars generally are equipped with LSDs. If on the other hand it is a front wheel drive car it will, because of these both added effects, ultimately end up under steering even though there also in this case will be advantageously differentiated longitudinal forces trying to counteract under steer. This latter reasoning shows that on principle the front wheel drive car almost cannot get too much of these differentiated longitudinal tire forces in acceleration situations. This fact together with the other above reasoning mean that one might argue that some form of ideal differential system will have the greatest benefit in front wheel drive cars. On the other hand it should be mentioned that differentiated longitudinal tire forces in a front axle can have its own problems in the form of torque steer effects meaning that torques and moments can transfer from the drive wheels to the steering wheel, which in itself can place special demands on the steering geometry etc.
Although we can get some performance- and some stability-benefits from the mentioned more advanced Limited Slip Differentials, all passive LSD variants are still to some extent a compromise between the ability to allow differentiation at the highest possible efficiency when that is appropriate but still have the ability to more or less fully lock any differentiation when that is the best for the performance and or stability of the vehicle.
For this reason the electronically controlled Limited Slip Differential (eLSD) has been developed. The eLSD generally has one multi plate clutch connected to an open differential and an actuator that, via an electronic control unit, can apply a controlled amount of clamping pressure to the clutch and thereby controlling the eLSD to be anything between fully open and fully locked.
Passenger cars, as a contrast to racing cars, are generally tuned to have a more under steering handling balance. The reasons for this are several but some of them are the facts that driving safety generally is higher on the priority list and performance is lower on the same list, passenger car drivers are also most often less experienced at driving at the handling limit which means that there is a need for a larger stability margin to help them cope with an eventual critical situation like a necessary evasive manoeuvre, especially at higher speeds when yaw damping is severely compromised and yaw over shoots are likely in response to sudden lane change manoeuvres etc. However, even if a vehicle is engineered to be quite severely under steering in steady state cornering situations it will generally still be possible to make it over steering and unstable in certain transient situations even though it will take more stability upsetting inputs to make it so, as compared to a vehicle with a more neutral handling balance. This fact together with the fact that a severely under steering vehicle might not always be considered the most fun to drive vehicle mean that vehicle engineers will have to come up with a compromise to the handling balance with regards to the partly conflicting characteristics of stability and driving pleasure.
In addition to the LSD- or eLSD-systems there are other systems that are even more effective at giving a more consistent handling balance irrespectively of the input torque. These systems are generally labelled “torque-vectoring” systems and can force the drive wheels to differentiate and thereby they have the ability to send more than half of the input torque to the one driving wheel with the highest rotational speed which is not possible with any kind of LSD which can only send more than half of the torque to the wheel with the lowest rotational speed or, if both wheels have the same rotational speed, to the wheel with the strongest resistance. However, these torque-vectoring systems are significantly more complex and therefore also more expensive. When it comes to the above mentioned compromise in handling balance there is also the possibility to use various kinds of stability control systems.
Stability control systems may be applied to help drivers prevent a vehicle from losing control in critical situations. Most vehicle stability control systems in the market are brake-based. Typically these brake-based stability control systems use a reference model to calculate the appropriate yaw rate, based on the longitudinal speed of the vehicle, the under steer gradient of the vehicle and the steering input of the driver. This reference yaw rate is continuously compared to the actual yaw rate of the vehicle in a closed loop manner (i.e. feed-back control) and if the two differ more than a certain amount, the so called dead band, the electronic control system can apply braking torque to one or more wheels to bring the vehicle back to the intended direction and specifically when it comes to over steer correction the normal way to decrease the yaw rate is to brake the corner outer front wheel. The mentioned dead band is needed to avoid too frequent an intervening from the system which would lead to an unnecessarily high wear rate of the brake system components as well as potentially being perceived as disturbing or intrusive by the driver since brake based stability control systems generally can be felt and heard when active and some drivers may think of this as being deprived of the control of the vehicle. It is generally known to the automotive industry that similar yaw resisting moments as in brake-based over steer correction can be achieved by controllable differentials like for example the eLSD.
Without any kind of stability control system (and an open differential), the stability of a vehicle is solely dependent on the lateral capacities of the tires whereas stability control systems, as already explained, tend to utilise differentiated longitudinal tire forces to influence the yaw rate of the vehicle. As also already explained the brake-based systems does this by braking individual wheels which except altering the yaw rate also lead to a speed decrease. Differential-based stability control on the other hand redistributes the already existing tire longitudinal forces of the driven wheels in response to the yaw rate of the vehicle which means, first of all, that it does not give a net speed decrease as the brake-based systems do and also that it works according to a “reactive” principle which means that the amount of yaw resisting moment about the yaw axis of the vehicle is dependent on the yaw rate itself. The former means that there is no real need for a dead band and the latter means that the amount of yaw resisting moment to quite a large extent is self-regulating which means that the control effort of the differential-based systems is lower than for the brake-based systems, that need to modulate the total rotational speed of a wheel via the powerful means of a wheel brake, instead of just modulating the relative rotational speed of both drive wheels of an axle via an actuator located within the drive-train between the wheels. Although the brake-based systems in many cases are able to ultimately generate a stronger yaw resisting moment there is a greater risk of for example over actuation if the [mu]-value estimation is incorrect.
Apart from the mentioned lower control demand of the differential-based systems there are two other theoretical benefits of really redistributing the present longitudinal forces instead of adding a brake force. The most obvious benefit is that there is no net speed decrease and hence no longitudinal load transfer that actually in itself gives a slight stability disturbing effect by decreasing the lateral capacity of the rear axle. The other benefit is the fact that redistributing the existing longitudinal tire forces means that there, as compared to braking the corner outer wheel, generally is less deterioration of the overall lateral capacity of the axle in which the intervention is made, for an equal amount of yaw resisting moment. Although it is possible to get a yaw resisting moment from a controlled differential in either axle it is also for the differential-based systems, despite of the above mentioned general benefits, still slightly more effective to make the intervention in the front axle. The main reasons for this are of course the facts that the front axle, in a potential over steer situation, is the axle with the highest lateral capacity margin and also that the small deterioration of lateral capacity resulting from the intervention in this case affects the front axle which in itself leads towards under steer.
When looking at how these two different approaches can be used to solve the same potential stability problems it is also quite obvious that there is a possibility to get positive synergy effects by using both principles in a way that the differential-based interventions are prioritized and the brake-based interventions kicks in only if and when the former proves not to be sufficient. The above mentioned benefits of redistributing the tire forces (instead of braking individual wheels) mean, irrespective of if the controllable differential is located in the front-axle, in the rear-axle or in both, that it can be used more often and that it generally will not be perceivable by the driver, all of which can help contributing to enhance both the performance of the vehicle as well as the driving experience. However, using controllable differential-based systems (like the eLSD) to improve vehicle stability means increased costs both regarding differential hard ware components and its required control system.
Consequently, in the field of vehicles, there is a need for improved methods and systems which are configured for increasing the stability of a road vehicle and also for adapting and controlling the yaw response, especially in the event of the driver applying large and sudden steering input during medium to high speed driving. There is also a need for this to be accomplished using low cost components and simple control.